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Photon: Quantum of Energy Photon ~ Quantum of Energy ~ Outline - Light as Waves - Light as Particles . Photoelectric Effect - photon energy . Compton Effect - photon momentum In physics, a quantum is the minimum unit of any physical entity involved in an interaction. The word comes from the Latin “quantus” for “how much.” Acknowledgement: Some of slides are adopted from PHY106 Particle Physics Module at Syracuse University by Dr. Steve Blusk 1 wavelength Light waves: Light Waves Characterized by: Amplitude (A) Frequency (ν) Wavelength (λ) amplitude Maxwell Showed us that Energy of EM wave ~ A2 EM FIELDS FOR WARMING EARTH EM FIELDS FOR LASER DRILLING Until about 1900, the classical wave theory of light described most observed Image by Metaveld BV http://commons. phenomena Image is in the public domain wikimedia.org/wiki/File:Lasersnijden_ 2 laserkop.jpg on Wikimedia Commons Are Photons Particles or Waves ? Newton believed that light was particles: • light travels in straight lines ! Light Source Barrier Particles Image by fotostijnl http://www. Produce flickr.com/photos/stijntje/20580 Image in public domain Straight 70484/ on flickr Shadows •what is ‘waving’ in an EM wave ? A wave is a vibration of some medium through which it propagates, e.g., water waves, waves propagating on a string Image is in the public domain 3 We described them as WAVES up till now Constructive Interference Incident light air oil water Young’s Double Slit Experiment Image in the Public Domain Coherent Light Sunlight Propagation From Direction Single Slit Waves Constructive Bend Into Destructive Interference Shadow Interference Barrier Screen Image by Pieter Kuiper http://commons. wikimedia.org/wiki/File:Compact-Disc-spectrum 4 Mercury.jpg on wikimedia commons Thomas Young’s Double Slit Experiment Interference is the defining ? characteristic of waves ? Partition with two very small thin slits (shown here greatly enlarged) Screen to let light through. But what happens when we reduce the intensity of incident light … everything should just get dimmer … Right ? Image is in the public domain 5 Photoelectric Effect . When light is incident on certain metallic surfaces, electrons are emitted from the surface – This is called the photoelectric effect – The emitted electrons are called photoelectrons . The effect was first discovered by Hertz . The successful explanation of the effect was given by Einstein in 1905 – Received Nobel Prize in 1921 for paper on electromagnetic radiation, of which the photoelectric effect was a part Classical Picture Quantum Picture --EM wave Photons -- Electrons Electrons shaken loose --knocked loose by an EM by photons wave 6 Photoelectric Effect Schematic Light . When light strikes E, photoelectrons are emitted . Electrons collected at C and A passing through the ammeter are a current in the circuit V . C is maintained at a positive potential by the power supply Variable Power Supply 7 Observation of the Photoelectric Effect … a Quantum Phenomenon “Classical” Method What if we try this ? Increase energy by Vary wavelength, fixed amplitude increasing amplitude electrons electrons emitted ? emitted ? No No No Yes, with low KE No Yes, with high KE No No electrons were emitted until the frequency of the light exceeded a critical frequency, at which point electrons were emitted from the surface ! (Recall:8 small λ large ν) Electron Energy as a Function of Frequency ωo frequency, ω SOLID VACUUM PHOTON BINDING ENERGY ELECTRON ENERGY OF KINETIC ELECTRON ENERGY 9 The Electromagnetic Spectrum Gamma SHORTEST WAVELENGTHS Rays (MOST ENERGETIC PHOTONS) According to quantum theory, a photon has an energy given by X Rays Ultraviolet Radiation Visible Light Infrared Radiation (Planck’s constant) Microwaves 10 photons have an energy equal to ten times that of a single photon Radio Waves LONGEST WAVELENGTHS (LEAST ENERGETIC PHOTONS) 10 So how do I reconcile wave and particle pictures? I thought that Maxwell’s equations described light … What is the connection between Maxwell’s equations and photons ? When to use classical Maxwell’s equations ? ? 11 Intensity Classical Intensity Intensity in terms of Photons 12 Coarseness Classical Maxwell’s equations: Fields can have any strength, even when weak Experiment: Light with finite power has limited number of photons Consequences for imaging and communication 13 PROBABILITY OF DETECTION OF EACH PHOTON PER UNIT AREA: PERUNIT OF EACHPHOTON OFDETECTION PROBABILITY We see that photons aredetectedwith We Consequences forImaging probability proportional to intensity Image by Rory Moynihan http://www.flickr.com/photo s/rtmoynihan/5613097441/ on flickr 14 Consequences for communication Figure by MIT OpenCourseWare Energy per bit photons terabit sec 15 Do Photons Have Momentum ? What is momentum ? Just like Energy, TOTAL MOMENTUM IS ALWAYS CONSERVED Photons have energy and a finite velocity so there must be some momentum associated with photons ! 16 Key Takeaways LIGHT ARRIVES IN INCREMENTS CALLED PHOTONS PHOTOELECTRIC EFFECT: PHOTON BINDING ENERGY ELECTRON (Planck’s constant) ENERGY OF KINETIC ELECTRON ENERGY LIGHT INTENSITY IN TERMS OF PHOTONS: PROBABILITY OF DETECTION OF EACH PHOTON PER UNIT AREA: Just like Energy, TOTAL MOMENTUM IS ALWAYS CONSERVED - Photon Momentum: 17 The Compton Effect In 1924, A. H. Compton performed an experiment where X-rays impinged on matter, and he measured the scattered radiation. Incident X-ray wavelength M A T Scattered X-ray T wavelength E R e Electron comes flying out Problem: According to the wave picture of light, the incident X-ray should give up some of its energy to the electron, and emerge with a lower energy (i.e., the amplitude is lower), but should have . It was found that the scattered X-ray did not have the same wavelength ! 18 Quantum Picture to the Rescue Electron Scattered X-Ray initially at Incident X-ray rest (almost) e e Ee Compton found that if you treat the photons as if they were particles of zero mass, with energy and momentum . The collision behaves just as if it were two billiard balls colliding ! Photon behaves like a particle with energy & momentum as given above! 19 Photon Momentum IN FREE SPACE: IN OPTICAL MATERIALS: 20 QUICK QUIZ A photon (quantum of light) is reflected from a mirror. … so is the following True or False: FALSE (A) Because a photon has a zero mass, it does not exert a force on the mirror. FALSE (B) Although the photon has energy, it cannot transfer any energy to the surface because it has zero mass. TRUE (C) The photon carries momentum, and when it reflects off the mirror, it undergoes a change in momentum and exerts a force on the mirror. FALSE (D) Although the photon carries momentum, its change in momentum is zero when it reflects from the mirror, so it cannot exert a force on the mirror. 21 Manifestation of the Photon Momentum SOURCE EMITTING A PHOTON photon Conservation of linear momentum implies that an atom recoils when it excited atom undergoes spontaneous emission. The direction of de -excited atom photon emission (and atomic recoil) is not predictable. A well-collimated atomic beam of excited atoms will spread laterally because of the recoil beam spreads laterally source of because of spontaneous associated with excited atoms collimating emission spontaneous emission. diaphragms SOURCE EMITTING AN EM WAVE A source emitting a spherical wave cannot recoil, because the spherical symmetry of the wave prevents it from carrying any linear momentum from the source. 22 Photon Momentum - Moves Solar Sails Image by D. Kassing http://en.wikipedia.org/wiki/File:SolarSail- Image in the Public Domain DLR-ESA.jpg on Wikipedia INCOMING PHOTONS SOLAR SAIL REFLECTED PHOTONS SOLAR SAIL 1000 W/m2 at rest 1000 W/m2 moves every second every second with photons with momentum photons with momentum momentum + (1000 J/m2)/c impact the sail - (1000 J/m2)/c leave the sail + (2000 J/m2)/c … and gets that much more Pressure acting on the sail = (2000 J/m2) /c /second = 6.7 Newtons/km2 momentum 23 every second … Classical Picture Quantum Picture - EM wave - Photons - - Electrons Electrons shaken loose - knocked loose - by an EM by photons wave Energy of EM wave ~ (Amplitude)2 Energy per photon photon momentum 24 MIT OpenCourseWare http://ocw.mit.edu 6.007 Electromagnetic Energy: From Motors to Lasers Spring 2011 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms..
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